If x is a negative integer and y is a positive integer, what is the value of \frac{|x - y|… — GMAT

If $x$ is a negative integer and $y$ is a positive integer, what is the value of $\frac{|x - y| - |y - x|}{x + y + 100}$ ?

Answer: 0

Answer

Given

x < 0

and

y > 0

, the quantity

x - y

is strictly negative, which means

|x - y| = -(x - y) = y - x

. The quantity

y - x

is strictly positive, so

|y - x| = y - x

. Thus, the numerator simplifies to

(y - x) - (y - x) = 0

. Dividing zero by any non-zero denominator yields

0

Step-by-Step Solution

Determine the signs of the terms inside the absolute value functions

Since

x < 0

and

y > 0

x - y < 0

and

y - x > 0

Subtracting a positive number from a negative number yields a negative value, while subtracting a negative number from a positive number yields a positive value.

Simplify the absolute value expressions

|x - y| = y - x

and

|y - x| = y - x

The absolute value of a negative number is its negation, and the absolute value of a positive number is the number itself.

Compute the difference in the numerator

|x - y| - |y - x| = (y - x) - (y - x) = 0

Subtracting an algebraic expression from an identical expression results in zero.

Evaluate the entire fraction

\frac{0}{x + y + 100} = 0

Zero divided by any non-zero real number is zero.

Key Concept

Positive and Negative Number Properties with Absolute Value

Question

Answer

Step-by-Step Solution

Key Concept

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